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Definition of Covariance

Covariance Image 1


A measure of the degree to which returns on two assets move in
tandem. A positive covariance means that asset returns move together; a
negative covariance means they vary inversely.


A statistical measure of the degree to which random variables move together.

Related Terms:

Serial covariance

The covariance between a variable and the lagged value of the variable; the same as

Correlation coefficient

A standardized statistical measure of the dependence of two random variables,
defined as the covariance divided by the standard deviations of two variables.

Country beta

covariance of a national economy's rate of return and the rate of return the world economy
divided by the variance of the world economy.

Homogenous expectations assumption

An assumption of Markowitz portfolio construction that investors
have the same expectations with respect to the inputs that are used to derive efficient portfolios: asset returns,
variances, and covariances.

Magic of diversification

The effective reduction of risk (variance) of a portfolio, achieved without reduction
to expected returns through the combination of assets with low or negative correlations (covariances).
Related: Markowitz diversification

Portfolio variance

Weighted sum of the covariance and variances of the assets in a portfolio.

Covariance Image 2

Correlation coefficient

A statistic in which the covariance is scaled to a
value between minus one (perfect negative correlation) and plus one (perfect
positive correlation).

Serial bonds

Corporate bonds arranged so that specified principal amounts become due on specified dates.
Related: term bonds.

Term bonds

Often referred to as bullet-maturity bonds or simply bullet bonds, bonds whose principal is
payable at maturity. Related: serial bonds

CARs (cumulative abnormal returns)

a measure used in academic finance articles to measure the excess returns an investor would have received over a particular time period if he or she were invested in a particular stock.
This is typically used in control and takeover studies, where stockholders are paid a premium for being taken over. Starting some time period before the takeover (often five days before the first announced bid, but sometimes a longer period), the researchers calculate the actual daily stock returns for the target firm and subtract out the expected market returns (usually calculated using the firm’s beta and applying it to overall market movements during the time period under observation).
The excess actual return over the capital asset pricing model-determined expected return market is called an ‘‘abnormal return.’’ The cumulation of the daily abnormal returns over the time period under observation is the CAR. The term CAR(-5, 0) means the CAR calculated from five days before the
announcement to the day of announcement. The CAR(-1, 0) is a control premium, although Mergerstat generally uses the stock price five days before announcement rather than one day before announcement as the denominator in its control premium calculation. However, the CAR for any period other than (-1, 0) is not mathematically equivalent to a control premium.

NPV (net present value of cash flows)

same as PV, but usually includes a subtraction for an initial cash outlay.

PV (present value of cash flows)

the value in today’s dollars of cash flows that occur in different time periods.
present value factor equal to the formula 1/(1 - r)n, where n is the number of years from the valuation date to the cash flow and r is the discount rate.
For business valuation, n should usually be midyear, i.e., n = 0.5, 1.5, . . .

Abnormal returns

Part of the return that is not due to systematic influences (market wide influences). In
other words, abnormal returns are above those predicted by the market movement alone. Related: excess

Acquisition of assets

A merger or consolidation in which an acquirer purchases the selling firm's assets.

Adjusted present value (APV)

The net present value analysis of an asset if financed solely by equity
(present value of un-levered cash flows), plus the present value of any financing decisions (levered cash
flows). In other words, the various tax shields provided by the deductibility of interest and the benefits of
other investment tax credits are calculated separately. This analysis is often used for highly leveraged
transactions such as a leverage buy-out.

Covariance Image 1


Any possession that has value in an exchange.

Asset/equity ratio

The ratio of total assets to stockholder equity.

Asset/liability management

Also called surplus management, the task of managing funds of a financial
institution to accomplish the two goals of a financial institution:
1) to earn an adequate return on funds invested, and
2) to maintain a comfortable surplus of assets beyond liabilities.

Asset activity ratios

Ratios that measure how effectively the firm is managing its assets.

Asset allocation decision

The decision regarding how an institution's funds should be distributed among the
major classes of assets in which it may invest.

Asset-backed security

A security that is collateralized by loans, leases, receivables, or installment contracts
on personal property, not real estate.

Asset-based financing

Methods of financing in which lenders and equity investors look principally to the
cash flow from a particular asset or set of assets for a return on, and the return of, their financing.

Asset classes

Categories of assets, such as stocks, bonds, real estate and foreign securities.

Asset-coverage test

A bond indenture restriction that permits additional borrowing on if the ratio of assets to
debt does not fall below a specified minimum.

Asset for asset swap

Creditors exchange the debt of one defaulting borrower for the debt of another
defaulting borrower.

Asset pricing model

A model for determining the required rate of return on an asset.

Covariance Image 2

Asset substitution

A firm's investing in assets that are riskier than those that the debtholders expected.

Asset substitution problem

Arises when the stockholders substitute riskier assets for the firm's existing
assets and expropriate value from the debtholders.

Asset swap

An interest rate swap used to alter the cash flow characteristics of an institution's assets so as to
provide a better match with its iabilities.

Asset turnover

The ratio of net sales to total assets.

Asset pricing model

A model, such as the Capital asset Pricing Model (CAPM), that determines the required
rate of return on a particular asset.


A firm's productive resources.

Assets requirements

A common element of a financial plan that describes projected capital spending and the
proposed uses of net working capital.

Average (across-day) measures

An estimation of price that uses the average or representative price of a
large number of trades.

Bond value

With respect to convertible bonds, the value the security would have if it were not convertible
apart from the conversion option.

Book value

A company's book value is its total assets minus intangible assets and liabilities, such as debt. A
company's book value might be more or less than its market value.

Book value per share

The ratio of stockholder equity to the average number of common shares. Book value
per share should not be thought of as an indicator of economic worth, since it reflects accounting valuation
(and not necessarily market valuation).

Capital asset pricing model (CAPM)

An economic theory that describes the relationship between risk and
expected return, and serves as a model for the pricing of risky securities. The CAPM asserts that the only risk
that is priced by rational investors is systematic risk, because that risk cannot be eliminated by diversification.
The CAPM says that the expected return of a security or a portfolio is equal to the rate on a risk-free security
plus a risk premium.

Carrying value

Book value.

Cash-surrender value

An amount the insurance company will pay if the policyholder ends a whole life
insurance policy.

Conflict between bondholders and stockholders

These two groups may have interests in a corporation that
conflict. Sources of conflict include dividends, distortion of investment, and underinvestment. Protective
covenants work to resolve these conflicts.

Continuous random variable

A random value that can take any fractional value within specified ranges, as
contrasted with a discrete variable.

Conversion value

Also called parity value, the value of a convertible security if it is converted immediately.

Current assets

value of cash, accounts receivable, inventories, marketable securities and other assets that
could be converted to cash in less than 1 year.

Discrete random variable

A random variable that can take only a certain specified set of discrete possible
values - for example, the positive integers 1, 2, 3, . . .

Dynamic asset allocation

An asset allocation strategy in which the asset mix is mechanistically shifted in
response to -changing market conditions, as in a portfolio insurance strategy, for example.

Endogenous variable

A value determined within the context of a model.

Excess returns

Also called abnormal returns, returns in excess of those required by some asset pricing model.

Exchange of assets

Acquisition of another company by purchase of its assets in exchange for cash or stock.

Exercise value

The amount of advantage over a current market transaction provided by an in-the-money

Exogenous variable

A variable whose value is determined outside the model in which it is used. Also called
a parameter.

Expected value

The weighted average of a probability distribution.

Expected value of perfect information

The expected value if the future uncertain outcomes could be known
minus the expected value with no additional information.

Extraordinary positive value

A positive net present value.

Extrapolative statistical models

Models that apply a formula to historical data and project results for a
future period. Such models include the simple linear trend model, the simple exponential model, and the
simple autoregressive model.

Face value

See: Par value.

Financial assets

Claims on real assets.

Firm's net value of debt

Total firm value minus total firm debt.

Fixed asset

Long-lived property owned by a firm that is used by a firm in the production of its income.
Tangible fixed assets include real estate, plant, and equipment. Intangible fixed assets include patents,
trademarks, and customer recognition.

Fixed asset turnover ratio

The ratio of sales to fixed assets.

Future value

The amount of cash at a specified date in the future that is equivalent in value to a specified
sum today.

Graham-Harvey Measure 1

Performance measure invented by John Graham and Campbell Harvey. The
idea is to lever a fund's portfolio to exactly match the volatility of the S and P 500. The difference between the
fund's levered return and the S&P 500 return is the performance measure.

Graham-Harvey Measure 2

Performance measure invented by John Graham and Campbell Harvey. The
idea is to lever the S&P 500 portfolio to exactly match the volatility of the fund. The difference between the
fund's return and the levered S&P 500 return is the performance measure.

Intangible asset

A legal claim to some future benefit, typically a claim to future cash. Goodwill, intellectual
property, patents, copyrights, and trademarks are examples of intangible assets.

Internal measure

The number of days that a firm can finance operations without additional cash income.

Intrinsic value of an option

The amount by which an option is in-the-money. An option which is not in-themoney
has no intrinsic value. Related: in-the-money.

Intrinsic value of a firm

The present value of a firm's expected future net cash flows discounted by the
required rate of return.

Investment value

Related:straight value.

Liquid asset

asset that is easily and cheaply turned into cash - notably cash itself and short-term securities.

Liquidation value

Net amount that could be realized by selling the assets of a firm after paying the debt.

Loan value

The amount a policyholder may borrow against a whole life insurance policy at the interest rate
specified in the policy.

Long-term assets

value of property, equipment and other capital assets minus the depreciation. This is an
entry in the bookkeeping records of a company, usually on a "cost" basis and thus does not necessarily reflect
the market value of the assets.

Limitation on asset dispositions

A bond covenant that restricts in some way a firm's ability to sell major assets.

Market value

1) The price at which a security is trading and could presumably be purchased or sold.
2) The value investors believe a firm is worth; calculated by multiplying the number of shares outstanding by the
current market price of a firm's shares.

Market value ratios

Ratios that relate the market price of the firm's common stock to selected financial
statement items.

Market value-weighted index

An index of a group of securities computed by calculating a weighted average
of the returns on each security in the index, with the weights proportional to outstanding market value.

Maturity value

Related: par value.

Measurement error

Errors in measuring an explanatory variable in a regression that leads to biases in
estimated parameters.

Negative amortization

A loan repayment schedule in which the outstanding principal balance of the loan
increases, rather than amortizing, because the scheduled monthly payments do not cover the full amount
required to amortize the loan. The unpaid interest is added to the outstanding principal, to be repaid later.

Negative carry

Related: net financing cost

Negative convexity

A bond characteristic such that the price appreciation will be less than the price
depreciation for a large change in yield of a given number of basis points.

Negative covenant

A bond covenant that limits or prohibits altogether certain actions unless the bondholders agree.

Negative duration

A situation in which the price of the MBS moves in the same direction as interest rates.

Negative pledge clause

A bond covenant that requires the borrower to grant lenders a lien equivalent to any
liens that may be granted in the future to any other currently unsecured lenders.

Net adjusted present value

The adjusted present value minus the initial cost of an investment.

Net asset value (NAV)

The value of a fund's investments. For a mutual fund, the net asset value per share
usually represents the fund's market price, subject to a possible sales or redemption charge. For a closed end
fund, the market price may vary significantly from the net asset value.

Net assets

The difference between total assets on the one hand and current liabilities and noncapitalized longterm
liabilities on the other hand.

Net book value

The current book value of an asset or liability; that is, its original book value net of any
accounting adjustments such as depreciation.

Net present value (NPV)

The present value of the expected future cash flows minus the cost.

Net present value of growth opportunities

A model valuing a firm in which net present value of new
investment opportunities is explicitly examined.

Net present value of future investments

The present value of the total sum of NPVs expected to result from
all of the firm's future investments.

Net present value rule

An investment is worth making if it has a positive NPV. Projects with negative NPVs
should be rejected.

Net salvage value

The after-tax net cash flow for terminating the project.

Non-reproducible assets

A tangible asset with unique physical properties, like a parcel of land, a mine, or a
work of art.

Normal random variable

A random variable that has a normal probability distribution.

Original face value

The principal amount of the mortgage as of its issue date.

Other current assets

value of non-cash assets, including prepaid expenses and accounts receivable, due
within 1 year.

Par value

Also called the maturity value or face value, the amount that the issuer agrees to pay at the maturity date.

Parity value

Related:conversion value

Performance measurement

The calculation of the return realized by a money manager over some time interval.

Policy asset allocation

A long-term asset allocation method, in which the investor seeks to assess an
appropriate long-term "normal" asset mix that represents an ideal blend of controlled risk and enhanced

Positive carry

Related:net financing cost

Positive convexity

property of option-free bonds whereby the price appreciation for a large upward change
in interest rates will be greater (in absolute terms) than the price depreciation for the same downward change
in interest rates.

Positive covenant (of a bond)

A bond covenant that specifies certain actions the firm must take. Also called
and affirmative covenant.

Positive float


Present value

The amount of cash today that is equivalent in value to a payment, or to a stream of payments,
to be received in the future.

Present value factor

Factor used to calculate an estimate of the present value of an amount to be received in
a future period.

Present value of growth opportunities (NPV)

Net present value of investments the firm is expected to make
in the future.







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